~*Algebra*~
Section 5-2
Vocabulary:
- Direct variation- is described as an equation in the form y=kx
- Constant variation- k is the constant variation in y=kx
- Family of graphs- is where graphs and equations of graphs have at least one common characteristic
- Parent Graph- the simplest graph in a family of graphs
Examples:
~ How Do You Graph This?
y=5x
1. Write k as a ratio, 5/1.
2. Graph the point (0,0).
3. From (0,0) go up five and over 1, representing rise over run.
4. Connect the dots, showing the slope.
~ How Do You Graph This?
y=-1/5x
1. K is already written as a ratio, - 1/5.
2. Graph (0,0)
3. From (0,0) go down 1 and over 5, representing rise over run.
4. Connect the dots, showing the slope.
~ Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
If y=21 when x=3, find x when y=-7
1. Using the direct variation equation fill in what your given, which is your y (21) and your x (3). So 21=k(3)
2. Next, divide by 3 on each side. So 21=k(3)
3 3
3. When you solve, 7=k. Then you put 7 into your direct variation equation. So, y=7x.
4. That's the first part of the problem. Next you find x when y= -7. Because you know your y (-7) and your k (7), you can fill in your equation. When you fill it in you get
-7=7x.
5. You divide each side by 7, -7=7x resulting in the answer, x= -1.
7 7
~ Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
If y=-42 when x=-7 ,find y when x=11
1. Using the direct variation equation fill in what your given, which is your y (-42) and your x (-7). So -42=k(-7)
2. Next, divide by -7 on each side. So -42=k(-7)
-7 -7
3. When you solve, 6=k. Then you put 6 into your direct variation equation. So y=6x.
4. That's the first part of the problem. Next, you find y when x=11. Because you know your x (11) and your k (6), you can fill in your equation. When you fill it in you get y=6(11).
5. When you solve, you get y=66.
Additional Information:
Direct Variation, where k is greater than 0
Graph y=6x
Step one Write the slope (in red) as a ratio. 6 = 6/1 rise/run
Step two Graph (0,0) on your coordinate plane. *Remember: (0,0) is also called the origin, the spot on the coordinate plane where the x- and y-axis cross.
Step three From the point (0,0) rise up 6 units and run right 1 unit.
Step four Draw a line connecting the points
Name the constant variation given these two points.
(3,8) (-2,3)
M=Y2-Y1/X2-X1
M= 3-8/-2-3
M= -5/-5
M= -1
So the constant variation is -1
Direct Variation Equation
Suppose you are traveling across the country and you travel for 5 hours and get 275 miles from your starting point.
Take your equation d=rt
275=r5 now solve for R
275/5=r5/5
55= r
so in on hour you travel 55 miles of course meaning you were going 55 mhp
Online resources:
Pictures:
This page by: ACR ~*LMH*~ and N something D
